In fact most of the desktop Macs are running the 32bit kernel by default. Only the Apple Xserve with proper CPUs will run the 64bit kernel by default.

The cause of that seems to be the fact that a lot of the drivers were not finished as 64bit version when Snow Leopard was ready. So Apple decided to deliver both kernels and boot the 32bit by default on the desktops.

However you can explicitly choose the 64bit kernel during boot by pressing the keys “6” and “4”. You can tell that you’re running the 64bit kernel by entering the following command in your Terminal:
uname -a